Would it be possible to make your game for Mac Linux and Windows
Yes the blend files can be opened on any system that can run blender. You can then export to game engine runtime on that system. You just need to check that they have the player installed as well, this should be included with release downloads but may not be for custom builds or graphicall downloads.

As gandlaf3 pointed out there is a new addon included with 2.72 that allows you to export to multiple platforms from your current system. You just need to enable the addon and test it. This is a new addon so be sure to report any trouble you have.

Be sure to pack all external files or include all external items for each platform.